Max Planck Lecture und MPI-IS Sommer Kolloquium 2022

K.K. Lee Professorin für Chemieingenieurwesen und Honorarprofessorin für Chemie, Materialwissenschaft und Ingenieurwesen, Lehrstuhl für Chemieingenieurwesen, Direktorin der Stanford Wearable Electronics Initiative (eWEAR)

Detaillierte Informationen über die Stuttgarter Max Planck Lecture kann hier nachgelesen werden: Lecture page.

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A challenge in data science is modeling 3-dimensional shapes such as a brain tumor or a bone. We introduce a representation of shapes that allows us to model shapes without requiring landmarks or assuming the shapes are diffeomorphic, we can also model shapes that are topologically different. We show that these transforms are injective on the space of shapes — each shape has a unique transform. We also provide a bound on the complexity of a  moduli space of shapes (characterized by bounds on critical points and curvature). We also introduce to date the most general shape space that has a mathematically rigorous definition, the construction is sheaf theoretic. We apply this representation to four statistical challenges: (1) computing the similarity between 3-dimensional shapes; (2) using the 3-dimensional shape as a covariate in regression problems; and (3) sub-image selection or what parts of the shape is associated to variation in a phenotype or trait, and (4) learning formal evolutionary models for shapes, that is estimating parameters like the selection pressure.

University Leipzig Center for Scalable Data Analytics and Artificial Intelligence, Max Planck Institute for Mathematics in the Sciences

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